Review of Adding and Subtracting Fractions for 3rd Grade

Master fraction operations: understanding parts of a whole, equivalent fractions, and addition/subtraction with like denominators through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Adding Fractions with Like Denominators
Exercise 1
Solve:
25 + 15 = ?
Definition:

Fraction: A number that represents part of a whole. It has a numerator (top number) and denominator (bottom number).

Like Denominators: Fractions with the same denominator (bottom number).

Addition method for like denominators:
  1. Keep the same denominator
  2. Add the numerators (top numbers)
  3. Write the sum over the common denominator
  4. Simplify if possible
Setup
25 + 15
Addition
35
Step 1: Check denominators

Both fractions have denominator 5, so they are like fractions

Step 2: Add numerators

2 + 1 = 3

Step 3: Keep the same denominator

Denominator stays 5

Step 4: Write the result

25 + 15 = 35

25 + 15 = 35
Final answer:

25 + 15 = 35

Applied rules:

• Like Denominators: When denominators are the same, add numerators only

• Keep Denominator: The denominator stays unchanged in the result

• Simplification: Reduce to lowest terms if possible (not needed here)

2 Subtracting Fractions with Like Denominators
Exercise 2
Solve:
78 - 38 = ?
Definition:

Subtracting Fractions: Finding the difference between two fractional amounts with the same whole.

Like Denominators: Fractions with the same denominator (bottom number).

Setup
78 - 38
Subtraction
48
Step 1: Check denominators

Both fractions have denominator 8, so they are like fractions

Step 2: Subtract numerators

7 - 3 = 4

Step 3: Keep the same denominator

Denominator stays 8

Step 4: Write the result

78 - 38 = 48

Step 5: Simplify if possible

48 = 12

78 - 38 = 12
Final answer:

78 - 38 = 12

Applied rules:

• Like Denominators: When denominators are the same, subtract numerators only

• Keep Denominator: The denominator stays unchanged in the result

• Simplification: Reduce to lowest terms by dividing numerator and denominator by their GCD

3 Word Problem with Fractions
Exercise 3
Emma ate 26 of a pizza for lunch. Later she ate another 16 of the pizza. What fraction of the pizza did Emma eat in total?
Definition:

Word Problems: Real-life situations that require mathematical operations to solve. We identify key information and determine which operations to use.

First part eaten
26
Second part eaten
16
Total eaten
36
Step 1: Identify the operation needed

"What fraction...in total?" indicates addition

Step 2: Set up the equation

26 + 16 = ?

Step 3: Add the fractions

Since denominators are the same: 26 + 16 = 36

Step 4: Simplify if possible

36 = 12

Emma ate 12 of the pizza
Final answer:

Emma ate 12 of the pizza

Applied rules:

• Problem Solving: Read carefully, identify key information, determine operations

• Like Denominators: When denominators are the same, add numerators only

• Simplification: Reduce to lowest terms by dividing numerator and denominator by their GCD

Key Concepts and Methods
ac + bc = a+bc
Adding Fractions with Like Denominators
Adding Fractions
ac + bc = a+bc
Like denominators
Subtracting Fractions
ac - bc = a-bc
Like denominators
Simplifying Fractions
ab = a÷gb÷g
Divide by GCD
Key definitions:

Numerator: The top number in a fraction (how many parts we have)

Denominator: The bottom number in a fraction (how many equal parts the whole is divided into)

Like Denominators: Fractions with the same denominator

Unlike Denominators: Fractions with different denominators (not covered in grade 3)

Adding Fractions Method:
  1. Check that denominators are the same
  2. Add the numerators
  3. Keep the denominator the same
  4. Simplify if possible
Subtracting Fractions Method:
  1. Check that denominators are the same
  2. Subtract the numerators
  3. Keep the denominator the same
  4. Simplify if possible
Tip 1: Only add or subtract the numerators when denominators are the same
Tip 2: Use visual models like pie charts or rectangles to understand fraction addition
Tip 3: Always simplify your final answer to lowest terms
Common errors: Adding denominators, forgetting to simplify, treating unlike denominators as like.
Equivalent fractions: 24 = 12 because they represent the same amount.
Detailed Summary: Adding and Subtracting Fractions
PartsWhole
Fraction Concept
Core Concepts:

Definition: A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number).

Numerator: Tells us how many parts we have

Denominator: Tells us how many equal parts the whole is divided into

Like Denominators: Fractions with the same denominator can be added or subtracted directly

Step-by-Step Process:
  1. Identify like denominators: Check if all fractions have the same denominator
  2. Perform operation on numerators: Add or subtract the numerators only
  3. Keep denominator: The denominator stays the same in the result
  4. Simplify: Reduce the fraction to lowest terms if possible
Example 1 (Simple): 14 + 24 = 34
Example 2 (With simplification): 26 + 16 = 36 = 12
Example 3 (Subtraction): 58 - 38 = 28 = 14
Key Rules: 1) Only add/subtract numerators when denominators are the same 2) Denominator stays unchanged 3) Always simplify final answer
Common Mistakes: Adding denominators, forgetting to simplify, not recognizing like denominators
Memory Aids:

• Remember: "Same Bottom, Add the Tops" for addition

• Remember: "Same Bottom, Subtract the Tops" for subtraction

• Always Check: Does your answer make sense compared to the original fractions?

• Simplify Rule: Divide numerator and denominator by their greatest common divisor

Properties and Advanced Strategies
ac + bc = a+bc
Commutative Property
Key properties:

Commutative Property: Order doesn't matter in addition (ac + bc = bc + ac)

Identity Property: Adding zero doesn't change the fraction (ac + 0c = ac)

Subtraction as Addition: ac - bc is the same as ac + (-bc)

Mental Math Strategies:
  1. Unit Fractions: Focus on how many parts you have
  2. Make One: Combine fractions that add up to 1 (e.g., 23 + 13 = 1)
  3. Compensation: Adjust to make calculations easier
Tip 1: To add 14 + 34, think "1 part plus 3 parts equals 4 parts out of 4 = 1 whole"
Tip 2: Always check if your answer is reasonable (e.g., adding two small fractions shouldn't give a result greater than 1 unless expected)
Tip 3: Use visual models (pie charts, rectangles) to verify your calculations
Tip 4: Know your basic fraction facts (e.g., 12 + 12 = 1)
Equivalent Fractions: 24 = 12 = 48 (same value, different representation)
Improper Fractions: When numerator > denominator (e.g., 54), it's more than 1 whole
Important Patterns:

• Adding Fractions: Increases the total amount

• Subtracting Fractions: Decreases the total amount

• Same Denominator: The key requirement for direct addition/subtraction

• Simplification: Always reduce to lowest terms for the final answer

Questions & Answers

Question: My students get confused about when they can add numerators directly. How do I help them understand like vs unlike denominators?

Answer: This is a very common challenge! Here are strategies to help students understand:

  • Concrete Examples: Use real objects - "You can add 2 apples + 3 apples, but not 2 apples + 3 oranges. Similarly, 25 + 35 works because both are fifths."
  • Visual Models: Draw circles divided into equal parts to show why denominators must match
  • Memory Device: "Same Bottom, Add the Tops!" - emphasize that denominators must be the same
  • Hands-on Activities: Use fraction tiles or pie pieces to physically combine like-sized pieces

For unlike denominators (advanced concept), explain that we need to find equivalent fractions with the same denominator first.

Question: How can I help my child understand when to simplify fractions after adding or subtracting?

Answer: Simplification is an important skill! Here's how to teach it:

  • Find Common Factors: Look for numbers that divide evenly into both numerator and denominator
  • Division Method: Divide both numerator and denominator by the same number
  • Greatest Common Divisor (GCD): Divide by the largest number that goes into both evenly
  • Check for Primes: If numerator and denominator are both prime numbers, it's already simplified

Example: 48 → Both 4 and 8 can be divided by 4 → 12. Practice with small numbers first, then gradually increase complexity.

Question: I sometimes forget whether to add or subtract the denominators. How do I remember the rule?

Answer: This is a very common question! Here's a simple way to remember:

  • Denominators Stay the Same: The denominator tells us what kind of pieces we're working with (halves, thirds, fourths, etc.)
  • Only Add/Subtract Numerators: We're counting how many pieces we have, not changing what kind of pieces they are
  • Memory Device: "Bottom stays put, top gets the action!"
  • Real Example: If you have 2 slices of pizza (each slice is 1/8 of the pizza) and get 3 more slices, you have 5 slices total (5/8 of the pizza). The slices are still eighths!

Always keep the denominator the same when adding or subtracting fractions with like denominators!